1. Field of the Invention
The present invention relates to generation of a halftone screen and image processing using the halftone screen.
2. Description of the Related Art
[Error Diffusion Method]
Many printers such as ink-jet printers use a tone reproduction method based on an error diffusion method. The error diffusion method diffuses errors generated upon binarizing image data to pixels to be binarized. As a result, since the error diffusion method can preserve local densities, and provides excellent resolution and image sharpness, it can satisfactorily reproduce tonality.
FIG. 1 is a block diagram showing the signal processing sequence by the error diffusion method.
A binarizing unit 22 binarizes N-th input pixel data X[n] and outputs output pixel data Y[n]. An error detector 27 outputs an error (difference) generated upon binarization of the input pixel data X[n] as error data Ye[n]. An error diffusion matrix 25 diffuses the error data Ye[n] to non-binarized pixels (pixels to be binarized). An adder 21 adds diffusion data Xe[n] output from the error diffusion matrix 25 to pixel data of the non-binarized pixels to which an error is to be diffused.
FIG. 2 is a view showing the relationship between non-binarized pixels and diffusion intensities.
A pixel indicated by symbol X is a pixel of interest of binarization, x indicates the main scan direction of recording, and y indicates the sub-scan direction of recording. A hatched part above the pixel X of interest indicates binarized pixels X (those after binarization), and a part below the pixel of interest indicates non-binarized pixels. A numerical value given to each non-binarized pixel indicates a diffusive ratio, 7/48 of the error data Ye[n] are diffused to pixels which neighbor the pixel X of interest in the x- and y-directions, and 5/48 of the error data Ye[n] are diffused to obliquely lower right and lower left pixels of the pixel X of interest.
The spatial frequency characteristic of an image that has undergone such an error diffusion method indicates a so-called blue noise characteristic with low spectrum intensity in a low-frequency region. The blue noise characteristic generally has an excellent resolution characteristic since the spatial frequency characteristic extends up to a high-frequency region, and exhibits satisfactory tone reproducibility since the densities of the image are locally preserved due to re-use of errors generated by binarization. Therefore, the error diffusion method is popularly used in ink-jet printers. However, the error diffusion method is not practically used in an electrophotographic printer since a stable output cannot be obtained for the following reasons.
An electrophotographic printer has an exposure process that scans a light beam to remove electric charges from a uniformly charged surface layer of a photosensitive drum of, for example, an organic photoconductor (OPC) or amorphous silicon. This exposure process has nonlinearity. Complexity of electrophotography processes including development, transfer, and fixing also causes nonlinearity.
An interference occurs between print dots due to this nonlinear characteristic, thus considerably impairing tonality. For example, even when one independent dot is to be printed, it is difficult to record such dot. On the other hand, dots can be surely recorded in a cluster state of several dots. For this reason, the high-frequency characteristic lowers, and the tonality of a highlight region of an image deteriorates.
If the distance between dots is small, toner may move to connect dots. In the processes for recording dots by attaching ink drops onto a medium like in the ink-jet system, although a micro phenomenon between inks and a medium occurs, an interference between print dots hardly occurs, and dots can be surely recorded.
As described above, an electrophotographic printer is weak in variations of the spatial frequency of an image due to the nonlinearity of the electrophotography processes, and the error diffusion method cannot be applied to the electrophotographic printer intact.
[AM Modulation Method]
An electrophotographic printer uses a halftone formation method based on halftone dots or halftone screen using a cluster of dots (to be referred to as a cluster halftone screen hereinafter) upon reproducing an image having tonality in consideration of the nonlinearity. That is, printing has to be done by limiting the spatial frequency to a certain frequency region to lower high-frequency components.
An AM modulation method based on a halftone dot method makes a fundamental frequency constant depending on the grid intervals of halftone dots, and can obtain stable tone reproducibility even in the electrophotography system. On the negative side, in color printing, moiré is readily generated due to overlaying of toners of C, M, Y, and K colors.
In order to suppress moiré, different screen angles are set for respective color components to drive moiré beats generated between color components to a high-frequency region, thus visually obscuring moiré. For example, a Y screen angle is set to be 30°, and C, M, and K screen angles are set to be 0 or 60°, thereby suppressing moiré due to overlaying of color components.
In digital halftone processing, since the resolution of a digital image is discrete, arbitrary screen angles cannot be set. However, by selecting optimal and discrete screen angles for respective color components, moiré can be suppressed.
Even upon optimization by introducing screen angles, moiré beats are merely driven to a high-frequency region, and a unique pattern generated due to overlaying of color components still remains. This is a so-called Rosetta pattern and becomes an obstacle upon outputting an image with high image quality. In particular, upon outputting an image with high image quality, smooth image quality reproduction like a photograph of silver halide processes is required, and such a Rosetta pattern is a serious obstacle in meeting this requirement.
[FM Modulation Method]
As another approach, a method of reproducing tonality by an FM modulation method using error diffusion or blue noise mask is known. Since the FM modulation method can randomly lay out print dots, has satisfactory tonality, and is free from any moiré due to overlaying of color components, it is popularly adopted in an ink-jet system, thermal transfer system, and the like. However, with the FM modulation method, the dot intervals change, and cannot be freely controlled. For example, the dot interval is gradually reduced with increasing density value. For this reason, the spatial frequency characteristic extends up to a high frequency region, and the FM modulation method is directly influenced by the frequency characteristic of a printer. Therefore, the FM modulation method is not suited to an electrophotographic printer which is susceptible to the influence of spatial frequency variations.
[Green Noise Method]
As a method that can solve these problems, a green noise method is known. Details of the green noise method are described in Daniel L. Lau and Gonzalo R. Arce, “Modern Digital Halftoning (Signal Processing and Communications)”, and U.S. Pat. No. 6,798,537. Note that “green noise” is named since the signal distribution frequency region is included in an intermediate frequency region with respect to white noise and blue noise.
FIG. 3 is a block diagram for explaining the signal processing sequence based on the green noise method.
A binarizing unit 22 binarizes N-th input pixel data X[n] and outputs output pixel data Y[n]. An error detector 27 outputs an error (difference) generated upon binarization of the input pixel data X[n] as error data Ye[n]. An error diffusion matrix 25 diffuses the error data Ye[n] to non-binarized pixels. An adder 21 adds diffusion data Xe[n] output from the error diffusion matrix 25 to pixel data of the non-binarized pixels to which an error is to be diffused. The processes described so far are the same as those in the error diffusion method shown in FIG. 1.
A calculation unit 23 acquires the values of a plurality of binarized pixels (to be referred to as reference pixels hereinafter), and applies a predetermined calculation to the acquired values. A gain adjuster 24 calculates data Xh[n] by multiplying data output from the calculation unit 23 by a predetermined gain h. An adder 26 adds the data Xh[n] to the pixel data output from the adder 21. The binarizing unit 22 inputs pixel data Xk[n] (feedback amount) to which the error and data Xh[n] are added.
FIG. 4 is a view showing the relationship between reference pixels and reference intensities.
As in FIG. 2, a pixel indicated by symbol X is a pixel of interest of binarization, x indicates the main scan direction of recording, and y indicates the sub-scan direction of recording. A hatched part above the pixel X of interest indicates binarized pixels. Binarized pixels indicated by a0, a1, a2, and a3 are reference pixels, and values a0, a1, a2, and a3 indicate reference intensities. Note that the reference pixels are binarized pixels in the vicinity of the pixel X of interest, and the image quality changes largely depending on selected reference pixels. A reference intensity ai=0 represents that data of the corresponding binarized pixel is not referred to, and the reference intensities are normalized assuming Σai=1. The output from the gain adjuster 24 is given by:Xh[n]=h×Σi(ai×Yi)   (1)where h is a gain coefficient, and
Yi is the value (0 or 255) of the i-th reference pixel.
[Binarization Result by Green Noise Method]
FIG. 5 is a view showing an image before binarization, and shows a grayscale image, the pixel values of which smoothly change from 0 (left end) to 255 (right end).
FIG. 6 is a view showing the binarization result of the grayscale image shown in FIG. 5 by the green noise method. In FIG. 6, error diffusion coefficients use those of Jarvis shown in FIG. 4, and the gain coefficient of the gain adjuster 24 is h=0.2. FIG. 7 is a view showing the relationship between reference pixels and reference intensities. In FIG. 7, binarized pixels which neighbor the pixel X of interest in the main scan direction and sub-scan direction are referred to at an intensity ratio 1:1. An image shown in FIG. 6 indicates an output image, the tonality of which is expressed by dots clustered by the green noise method.
FIGS. 8A to 8C are views showing changes of the output image when the gain coefficient h is changed upon binarizing the grayscale image shown in FIG. 5 by the green noise method.
FIG. 8A shows an output image example that does not input any feedback from binarized pixels by setting h=0. In this case, the output image is obtained by the error diffusion method using the error diffusion coefficients of Jarvis.
FIGS. 8B and 8C respectively show output image examples when h=0.2 and h=0.4. As the gain coefficient h becomes larger, the cluster sizes become larger, and an image apparently having high graininess is formed. In other words, as can be seen from FIGS. 8B and 8C, green noise shifts toward a low-frequency region as the gain coefficient h becomes larger. That is, the frequency characteristic of noise extended to a high-frequency region by the error diffusion method can be reduced to a spatial frequency region that can be stably handled by the electrophotography system by increasing the gain coefficient h. By adopting the green noise method, very close dots are controlled to form a cluster so as to avoid an unstable spatial frequency region of the electrophotography system, and image formation in a stable spatial frequency region can be made.
However, as can be seen from the image shown in FIG. 8C, dot patterns form parallel line-like patterns at an equal interval in a certain density region, and randomness of clustered dots (to be referred to as cluster dots) is lost.
FIG. 9 is a view showing a spectrum pattern by two-dimensional Fourier transformation of the image shown in FIG. 8C. White regions in FIG. 9 indicate spectra having high intensities. As can be seen from FIG. 9, a two-dimensional spectrum distribution does not have an isotropic ring pattern, but it exhibits strong spectra in a certain direction (in a direction from upper left to lower right in FIG. 9). This reflects the spectra of the parallel line-like patterns of the image shown in FIG. 8C.
FIG. 10 is a graph showing the spectral intensities of a section along the ordinate of the spectrum pattern shown in FIG. 9, which is slightly on the right side of the center. A pattern of spectral intensities shows asymmetry to have a zero frequency (at the position of 128 on the abscissa of FIG. 10) as the center.
Generation of the periodic parallel line-like patterns adversely affects moiré avoidance. When dots which are to be randomly distributed originally form periodic patterns in a certain density region, periodic patterns of other colors overlap on that density region, thus generating moiré. Screens of the FM modulation method aim at a high-image quality output free from any moiré, and generation of moiré poses a serious problem.